Algorithmic Specified Complexity

Abstract

Engineers like to think that they produce something different from that of a chaotic system. The Eiffel tower is fundamentally different from the same components lying in a heap on the ground. Mt. Rushmore is fundamentally different from a random mountainside. But engineers lack a good method for quantifying this idea. This has led some to reject the idea that engineered or designed systems can be detected. Various methods have been proposed, each of which has various faults. Some have trouble distinguishing noise from data, some are subjective, etc. For this study, conditional Kolmogorov complexity is used to measure the degree of specification of an object. The Kolmogorov complexity of an object is the length of the shortest computer program required to describe that object. Conditional Kolmogorov complexity is Kolmogorov complexity with access to a context. The program can extract information from the context in a variety of ways allowing more compression. The more compressible an object is, the greater the evidence that the object is specified. Random noise is incompressible, and so compression indicates that the object is not simply random noise. This model is intended to launch further dialog on use of conditional Kolmogorov complexity in the measurement of specified complexity.